Courses in Mathematics

Mathematics

MATH-B 111 Mathematics for Business (3 cr)

With successful completion of this course, the student will have algebraic skills and tools that are used for problem-solving in the business professions and be prepared for MATH-M 118 (Finite Mathematics) and ECON-E 270 (Statistics). The college algebra topics will include, but not be limited to the following: Solving equations, functions, and inequalities; solving systems of linear equations; graphing of equations and functions; interpreting graphs/tables/charts of equations and functions; performing algebraic operations on polynomial, rational, radical expressions in one/several variables; development of mathematical model from a word problem; application of these algebraic concepts and skills in business applications.

  • Offered every Fall and Spring Semester.
  • Offered summer semester, occasionally.
  • Prerequisite: HS Algebra 2 or Skills Review Test.
  • Credit given only for one: MATH-H 111, MATH-E 111, MATH-S 111, MATH-M 123 or MATH-M 110
  • Open only to Business students.

MATH-E 111 Mathematics for Elementary Education (3 cr)

Designed for the elementary education student to develop skills in the use of numeration systems, number theory, set theory, logic, networks, systems of equations, and geometry. These skills will be useful in future teaching assignments and for passing the State of Indiana Praxis exam. The purpose of Math-E 111 is to provide the students with knowledge of the concepts, theories, and procedures in the mentioned areas. Offered every Fall and Spring semester.

MATH-H 111 Mathematics for the Humanities (3 cr)

Designed for the humanities student to provide a variety of topics in mathematics, including, but not limited to: numeration systems; geometry; financial management; statistics; set theory. The course also provides a general, historical perspective of mathematics and development of practical application skills. Emphasis will be placed on mathematical modeling and solving word problems.

  • Offered every Fall and Spring semester.
  • Credit given only for one: MATH-H 111, MATH-E 111, MATH-S 111, MATH-M 123 or MATH-M 110
  • Prerequisite: HS Algebra 2 or Skills Review Test.
  • As of Fall 2013 this course replaces MATH-M 110.
  • May use this course to FX a previously taken MATH-M110.
  • Open to Humanities students only.

MATH-L 111 Mathematics Laboratory for Business, Social Science, Nursing (2 cr)

A mathematics laboratory course to be taken concurrently with MATH-B 111 or MATH-N 111. (See course description for MATH-B 111 or MATH-N 111.) Designed to prepare you for MATH-M 118 and statistics.

  • Not distribution satisfying.
  • Offered every Fall and Spring semester.
  • Co-requisite: MATH-B 111 or MATH-N 111.

MATH-N 111 Mathematics for Nursing (3 cr)

With successful completion of this course, the student will have algebraic skills and tools that are used for problem-solving in the nursing profession and be prepared for NURS-H 355 (Data Analysis) ) and the nursing math test. The college algebra topics will include, but not be limited to the following: Solving equations, functions, and inequalities; solving systems of linear equations; graphing of equations and functions; interpreting graphs/tables/charts of equations and functions; solving direct/ indirect variation and proportion equations; use of dimensional analysis; development of mathematical model from a word problem; application of these algebraic concepts and skills in nursing applications.

  • Offered every Fall and Spring semester.
  • Offered Summer semester, occasionally.
  • Prerequisite: HS Algebra 2 or Skills Review Test.
  • Credit given only for one: MATH-H 111, MATH-E 111, MATH-S 111, MATH-M 123 or MATH-M 110
  • Open only to Nursing students

MATH-S 111 Mathematics for Social Sciences (3 cr)

Designed for the social science student to provide math skills in problem-solving and reasoning for application in social science professions. To develop problem-solving and reasoning skills, mathematics topics may include, but are not limited to: logic (statements and truth tables), algebra of equations and graphing, elementary statistics, set theory, and counting & probability. Emphasis will be placed on mathematical modeling and solving word problems.

  • Offered every Fall and Spring semester.
  • Prerequisite: HS Algebra 2 or Skills Review Test.
  • Credit given only for one: MATH-H 111, MATH-E 111, MATH-S 111, MATH-M 123 or MATH-M 110
  • As of Fall 2016, this course replaces MATH-X111, Math for Social Sciences.
  • Open only to Social Science students.

MATH-X 111 Topics in Mathematics for Non-Majors (1-3 cr)

Designed to provide a variety of topics in mathematics, including, but not limited to: geometry; financial management; statistics; set theory; voting methods; celestial navigation; math of ancient civilizations. The course also provides a general, historical perspective of mathematics and development of practical application skills. Emphasis will be placed on mathematical modeling and solving word problems.

  • Offered periodically.
  • Prerequisite: HS Algebra 2 or Skills Review Test.
  • May be repeated with different topic.

MATH-K 300 Statistical Techniques for Health Professions (3 cr)

Course introduces nursing/health science students to the basic concepts and techniques of data analysis needed in professional health care practice. Measurements, data analysis and statistics are examined. Differences in types of qualitative data and methods of interpretation are explored. Procedures of estimation and hypothesis testing are also studied. Emphasis is on the application of fundamental conception to real situations in client care.

MATH-M 118 Finite Mathematics (3 cr)

Set theory, linear systems, matrices and determinants, probability, and linear programming. Applications to problems from business and the social sciences.

  • Offered every semester.
  • Prerequisite: Appropriate placement on skills review or MATH-M 123

MATH-M 119 Brief Survey of Calculus I (3 cr)

An introduction to calculus primarily for students in business and the social sciences.

  • Credit not given for both MATH-M 119 and MATH-M 215.
  • Offered summer semesters.
  • Prerequisite: Appropriate placement on skills review or MATH-M 125 Pre-calculus Mathematics.

MATH-M 120 Brief Survey of Calculus II (3 cr)

A continuation of MATH-M 119 covering topics in elementary differential equations, calculus of functions of several variables, and infinite series.

  • Intended for non-physical science students.
  • Credit not given for both MATH-M 216 and MATH-M 120.
  • Offered periodically.
  • Prerequisite: MATH-M 119

MATH-M 123 College Algebra (4 cr)

Designed to prepare you for MATH-M 125. Algebraic operations; polynomial, exponential, and logarithmic functions and their graphs; conic sections; systems of equations; and inequalities.

  • Offered every semester.
  • Prerequisite: Appropriate placement on skills exam

MATH-L 123 College Algebra Laboratory (2 cr)

Designed to prepare you for MATH-M 125. Laboratory component to be taken concurrently with MATH-M 123. (See course description above.)

  • Not distribution satisfying.
  • Offered every semester.
  • Co-requisite: MATH-M 123.

MATH-M 125 Pre-Calculus Mathematics (3 cr)

Designed to prepare you for MATH-M 215. Algebraic operations; polynomial, exponential, and logarithmic functions and their graphs; conic sections; systems of equations; and inequalities.

  • Offered every semester.
  • Prerequisite: Appropriate placement on skills exam, or MATH-M 123

MATH-M 126 Trigonometric Functions (2 cr)

Designed to prepare you for MATH-M 215. Trigonometric functions; identities. Graphs of trigonometric and inverse trigonometric functions.

  • Offered every semester.
  • Prerequisite: MATH-M 125 or equivalent (may be taken concurrently)

MATH-M 215 Analytic Geometry and Calculus I (5 cr)

Coordinates, functions, straight lines, limits, continuity, derivatives, definite integral, applications, circles, conics, techniques of integration, and infinite series.

MATH-M 216 Analytic Geometry and Calculus II (5 cr)

Coordinates, functions, straight lines, limits, continuity, derivatives, definite integral, applications, circles, conics, techniques of integration, and infinite series.

MATH-M 295 Readings and Research (1-3 cr)

Supervised problem solving.

  • Offered periodically.
  • Prerequisite: Permission of a member of the mathematics faculty, who will act as supervisor.

MATH-M 301 Applied Linear Algebra (3 cr)

Emphasis on applications: systems of linear equations, vector spaces, linear transformations, matrices, simplex method in linear programming.

  • Computer used for applications.
  • Credit not given for both MATH-M 301 and MATH-M 303.
  • Offered periodically.
  • Prerequisite: MATH-M 216 or consent of instructor

MATH-M303 Linear Algebra for Undergrads. (3 cr)

Introduction to theory of real and complex vector spaces. Coordinate systems, linear dependence, and bases. Linear transformations and matrix calculus. Determinants and rank.

  • Credit not given for both MATH-M 301 and MATH-M 303.
  • Offered fall and spring semesters.
  • Prerequisite: MATH-M 216 or consent of instructor

MATH-M 311 Calculus III (3 cr)

Elementary geometry of 2, 3, and n-space, functions of several variables, partial differentiation, minimum and maximum problems, and multiple integration.

  • Offered every semester.
  • Prerequisite: MATH-M216 or consent of instructor

MATH-M 312 Calculus IV (3 cr)

Differential calculus of vector-valued functions, transformation of coordinates, change of variables in multiple integrals. Vector integral calculus: line integrals, Green’s theorem, surface integrals, Stokes’s theorem. Applications.

  • Offered periodically.
  • Prerequisite: MATH-M 311 or consent of instructor

MATH-M 313 Elementary Differential Equations with Applications (3 cr)

Ordinary differential equations of first order and linear equations of higher order with applications, series solutions, operational methods, Laplace transforms, and numerical techniques.

  • Offered summer semesters.
  • Prerequisite: MATH-M 216 or consent of instructor.

MATH-M 366 Elements of Statistical Inference (3 cr)

Sampling distributions (chi-square, T and F distributions), order statistical decisions and inference. Hypothesis-testing concepts, Neyman-Pearson lemma, likelihood ratio tests, power of tests. Point estimation, method of moments, maximum likelihood, Cramer-Rao bound, properties of estimators. Regression, correlation, analysis of variance, non-parametric methods.

  • Offered fall semesters, and occasionally spring.
  • Co or Prerequisite: MATH-M 215.

MATH-M 371 Elem. Computational Methods (3 cr)

Interpolation and approximation of functions, solution of equations, numerical integration, and differentiation. Errors, convergence, and stability of the procedures. You will write and use programs applying numerical methods.

  • Offered fall semesters.
  • Prerequisite: MATH-M 216, or consent of instructor.

MATH-M 380 History of Mathematics (3 cr)

Brief study of the development of algebra and trigonometry; practical, demonstrative, and analytic geometry; calculus, famous problems, calculating devices; famous mathematicians in these fields and chronological outlines in comparison with outlines in the sciences, history, philosophy, and astronomy.

  • Offered fall semesters.
  • Prerequisite: MATH-M215 or consent of instructor.

MATH-M 393 Bridge to Abstract Mathematics (3 cr)

Preparation for 400 level math courses. Teaches structures and strategies of proofs in a variety of mathematical settings: logic, sets, combinatorics, relations and functions and abstract algebra.

MATH-M 403 Introduction to Modern Algebra I (3 cr)

Study of groups, rings, fields (usually including Galois theory), with applications to linear transformations.

MATH-M 404 Introduction to Modern Algebra II (3 cr)

Study of groups, rings, fields (usually including Galois theory), with applications to linear transformations.

  • Offered periodically in summer semesters.
  • Prerequisite: MATH-M 403 or consent of instructor

MATH-M 405 Number Theory (3 cr)

Numbers and their representation, divisibility and factorization, primes and their distribution, number theoretic functions, congruencies, primitive roots, diophantine equations, quadratic residues, and sums of squares.

  • Offered summer semester.
  • Prerequisite: MATH-M 216 or consent of instructor.

MATH-M 406 Topics in Mathematics (3 cr)

Selected topics in various areas of mathematics which are not covered by the standard courses.

  • May be repeated for credit.
  • Offered periodically.

MATH-M 413 Introduction to Analysis I (3 cr)

Modern theory of real number system, limits, functions, sequences and series, Riemann-Stieltjes integral, and special topics.

MATH-M 414 Introduction to Analysis II (3 cr)

Modern theory of real number system, limits, functions, sequences and series, Riemann-Stieltjes integral, and special topics.

MATH-M 421 Introduction to Topology I (3 cr)

Introduction to point set topology with emphasis on metric spaces. Continuity, Cartesian products, connectedness, compactness, completeness. Elements of homotopy theory, fundamental group and covering spaces, elementary homology theory, applications to simplicial complexes and manifolds.

MATH-M 422 Introduction to Topology II (3 cr)

Introduction to point set topology with emphasis on metric spaces. Continuity, Cartesian products, connectedness, compactness, completeness. Elements of homotopy theory, fundamental group and covering spaces, elementary homology theory, applications to simplicial complexes and manifolds.

MATH-M 447 Math Models & Applications I (3 cr)

Formation and study of mathematical models used in the biological, social, and management sciences. Mathematical topics include games, graphs, Markov and Poisson processes, mathematical programming, queues, and equations of growth.

MATH-M 448 Math Models & Applications II (3 cr)

Formation and study of mathematical models used in the biological, social, and management sciences. Mathematical topics include games, graphs, Markov and Poisson processes, mathematical programming, queues, and equations of growth.

  • Offered periodically in spring semesters.
  • Prerequisites: MATH-M 447.

MATH-M 451 The Mathematics of Finance (3 cr)

Course covers probability theory, Brownian motion, Ito’s Lemma, stochastic differential equations, and dynamitic hedging. These topics are applied to the Black-Scholes formula, the pricing of financial derivatives, and the term theory of interest rates.

MATH-M 463 Introduction to Probability Theory I (3 cr)

The meaning of probability. Random experiments, conditional probability, independence. Random variables, expected values and standard deviations, moment generating functions, important discrete and continuous distributions. Poisson processes. Multivariate distributions, basic limit laws such as the central limit theorem.

  • Offered periodically in spring semesters.
  • Prerequisites: MATH-M 303 and MATH-M 311 or the consent of the instructor.

MATH-M 466 Introduction to Mathematical Statistics (3 cr)

Rigorous mathematical treatment of problems in sampling and statistical inference. Possible topics include sufficient statistics, exponential distributions, monotone likelihood ratio, most powerful tests, minimum variance estimates, shortest confidence intervals, linear models, maximum likelihood, simultaneous equations, the relationship of theory to practice.

  • No regular offerings.
  • Prerequisite: MATH-M 463 or consent of the instructor.

MATH-M 499 Senior Seminar (3 cr)

Students integrate their study of mathematics and explore the connections within fields of mathematics and other disciplines. Students usually create a portfolio that showcases their understanding of the areas of study within mathematics and their applications outside of mathematics. Alternatives may include internships or other projects, as approved by advisor.

  • Offered every fall and spring semester.
  • Prerequisite: Senior standing as a Mathematics Major.

Mathematics for Educators

MATH-T 321 Intuitive Topology (3 cr)

Intuitive description of topology, including networks and maps, topological equivalence, classification of surfaces, spheres with handles, Jordan curve theorem, transformations, and fixed-point theorems.

  • Offered periodically.
  • Prerequisite: MATH-M 216 or consent of instructor.

MATH-T 336 Topics in Euclidean Geometry (3 cr)

Axiom systems for the plane; the parallel postulate and non-Euclidean geometry; classical theorem. Geometric transformation theory; vectors and analytic geometry; convexity; theory of area and volume.

  • Offered summer semesters, odd years.
  • Prerequisite: MATH-M 216 or consent of instructor.

MATH-J 497 Internship in Teaching Collegiate Mathematics (1-3 cr)

Designed to provide an opportunity for students to teach basic algebra and observe with discussion instructional techniques at the collegiate level in preparation for further career development in teaching at a post-secondary level.

  • Prerequisite: Senior standing in Mathematics degree or Math Education degree; Consent of 2 math faculty; Minimum GPA 3.0.
  • Additional requirement: Teaching of a college level mathematics class

Graduate Courses

MATH-J 597 Internship in Teaching Collegiate Mathematics (1-3 cr)

Designed to provide an opportunity for students to teach 100 and 200 level undergraduate math courses and observe with discussion instructional techniques at the collegiate level in preparation for further career development in teaching at a post-secondary level.

  • Prerequisite: Open to MAT students only; Consent of 2 math faculty; Minimum GPA 3.0.
  • Additional requirement: Teaching of a college level mathematics class

MATH-M 501 Survey of Algebra (3 cr)

A continuation for the undergraduate sequence of Modern Algebra. Groups: Jordan-Holder theorem, Sylow theorems, Free Groups. Rings: Ideals and Factor Rings. Fields: Algebraic closure; separable and inseparable algebraic extensions; Galois Theory; finite fields, insolvability of the quintic.

  • Prerequisite: MATH-M 403 and MATH-M 404
  • Open to Graduate-Level Students only or Consent of Instructor

MATH-M 505 Basic Number Theory 1 (3 cr)

Congruencies, unites modulo n, lattices and abelian groups, quadratic residues, arithmetic functions, Diophantine equations, Farey fractions, continued fractions, partition function, the Sieve method, density of subsets of integers, c-function, the prime number theorem.

  • Open to Graduate-Level Students only or Consent of Instructor

MATH-M 511 Real Variables 1 (3 cr)

Sets and functions, cardinal and ordinal numbers, set functions, kinds of measures, integration, absolute continuity, convergence theorems, differentiation and integration.

  • Prerequisite: MATH-M 413 and MATH-M 414
  • Open to Graduate-Level Students only or Consent of Instructor

MATH-M 521 Topology 1 (3 cr)

Point-set topology including connectedness, compactness, separation properties, products, quotients, metrization, function spaces.

  • Prerequisite: MATH-M 413
  • Open to Graduate-Level Students only or Consent of Instructor

MATH-M 551 Markets and Asset Pricing (3 cr)

The concept of arbitrage and risk-neutral pricing are introduced within the context of dynamical models of stock prices, bond prices and currency exchange rates. Specific models include multi-period binomial models, Markov processes, Brownian motion and martingales.

MATH-M 563 Theory of Probability I (3 cr)

Basic concepts of measure theory and integration, axiomatic foundations of probability theory, distribution functions and characteristic functions, infinitely divisible laws and the central limit problem.

  • Prerequisite: MATH-M 413 and MATH-M 463
  • Open to Graduate-Level Students only or Consent of Instructor

MATH-M 571 Analysis of Numerical Methods I (3 cr)

Solution of systems of linear equations, elimination and iterative methods, error analyses, eigenvalue problems.

MATH-T 590 Seminar for Mathematics Teachers (3 cr)

A seminar course for students in the M.A.T. program. Emphasis on the interrelationship among mathematical topics, curriculum reform, professional growth, and classroom practice. Specific topic selected jointly with the instructor.

  • Open only to M.A.T. students.

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